# Optimal asset allocation

I apologize if similar question has been already asked.

I have to compute optimal allocation of investment I between market asset and risk free asset. The investor's utility function is $$U(w)=E(r_P)- γσ^2(r_P))/2$$, $$γ = 3$$.

Then I use two formulas:

$$E(r_P) = r_F + ((E(r_M) - r_F)σ_P)/σ_M$$

$$σ^2_P = w^2_1σ^2_1 + w^2_2σ^2_2 + 2w_1 w_2 σ_1 σ_2 ρ$$

Which I plug in the utility function, before taking the derivatives wrt $$w_1$$ & $$w_2$$ . The result I obtained after equating both FOC seems wrong, because I can't use $$γ = 3$$ information anywhere to solve the problem:

$$w_1 = ρ^2$$

So where's the mistake?

Also I don't know the code for fraction line, so sorry about the messy notation.

• I don't see $\beta$ appear in $U(w)$? – Bob Jansen Aug 28 '19 at 13:56
• I figured out that γ=3 and not β. – Svit Valenčič Aug 28 '19 at 17:01
• You can either self-answer or delete the question. I don't believe anyone can give a useful answer now. – Bob Jansen Aug 28 '19 at 20:14